Method and apparatus with improved estimation accuracy and robustness for fine frequency offset estimation in coherent receivers

ABSTRACT

The present disclosure provides a method and system for fine estimation of a local oscillator frequency offset of a received signal at a coherent receiver, by evaluating the probability mass function (PMF) of the signal phase of output symbols at different frequencies. At frequencies other than the actual frequency offset, the signal phase is uniformly distributed in [-π,π] such that the summation of a function of PMF values where the function is convex or concave between 0 and 1 can be utilized to determine an a frequency offset to be used by the coherent receiver.

CROSS-REFERENCE

This application is a Continuation-In-Part of U.S. patent application Ser. No. 14/603,890 filed on Jan. 23, 2015, the entirety of which is incorporated by reference herein.

FIELD

The present disclosure relates generally to determining frequency offset of a received signal in a data transmission system.

BACKGROUND

The delivery of data content to users, which can include for example Internet content, media content, and voice communications, is provided through a distributed data network. FIG. 1 is an example data network diagram showing how service provider 10 provides data content to end users at their homes or office buildings 12, or wherever they may be located. Depending on geographical area to be covered, various intermediate nodes may be required to distribute the data content to the end users 12. In the example of FIG. 1, regional nodes 14 can function as a data delivery node to users in vicinity of the regional nodes 14, and can function as a repeater for redistributing the data content received from the service provider 10 to base stations 16. Base stations 16 can be located in a neighborhood to facilitate delivery of data content to the homes or buildings 12 located nearby. The base stations 16 can be configured to provide wireless services to users as well. It should be appreciated that the number of intermediate nodes between the service provider 10 and the end users 12 can be adjusted depending on the required geographical coverage of the data services.

The medium for carrying the signals representing the data content between the nodes, such as between service provider 10 and the regional node 14, between the regional node 14 and the base stations 16, and between the base stations 16 and the homes or buildings 12 are data cables 18, 20 and 22. These data cables can be electrical conducting cables made of copper, or they can be optical cables which carry data in the form of modulated laser light. It is well known that optical cables have a much larger data bandwidth than copper cables, and have the benefit of low signal loss over long distances. That being said, optical data transmission is still subject to various phenomena which can distort the optical signal, and must be compensated for in order to recover the transmitted data.

FIG. 2 is a simplified diagram of an optical data transportation link 30, which includes a transmitter 32 and a coherent receiver 34 connected to each other by an optical propagation channel 36. Each pair of nodes shown in the example data network diagram of FIG. 1 can have the optical data transportation link 30 presently shown in FIG. 2.

The transmitter 32 generates an optical signal comprised of two orthogonal linear polarization components (X and Y), wherein each component is comprised of two orthogonal phase components (in-phase I and quadrature Q) that have the same carrier frequency. The carrier frequency is an optical wavelength supplied by a laser with phase noise. The propagation channel 36 is comprised of optical filters such as cascaded WSS, fiber, amplifiers that are the sources of chromatic dispersion (CD), nonlinear phase noise, polarization mode dispersion (PMD), polarization dependent loss (PDL), polarization dependent gain, polarization rotation and optical white Gaussian noise.

The coherent receiver 34 is comprised of an integrated coherent receiver, photo detectors (PIN), analog to digit converters (ADC) and a DSP unit. The integrated coherent receiver 34 is the place where a local oscillator (LO), with a frequency that is closely matched to the transmitter laser, mixes with a propagated optical signal and splits it to four signals with each being a mixture of transmitted signals. The DSP unit is where signals are processed and data are recovered. Further details of all the above mentioned components are discussed later.

One of the problems with optical transmission is frequency wander, where a frequency shift in the base band signal occurs relative to the frequency at the transmitter 32. This is referred to as local oscillator frequency offset (LOFO), and the resulting signal at the receiver 34 has a frequency that is not exactly matched with that of the transmitter 32. The LOFO needs to be corrected at the receiver 34 in order to recover data in the optical signal. In some currently known systems, the LOFO can be as large as ±5 GHz.

Most known solutions follow a two-step approach for determining the frequency offset of the received signal. First a coarse frequency offset estimator (FOE) can estimate and correct LOFO to less than ±1 GHz estimation error. Then a fine estimation is executed to determine the final LOFO with an estimation error of less than 10 MHz. However, most known fine LOFO estimator solutions are very complex and thus costly to implement, vulnerable to different types of impairments which increase the estimation error beyond an expected threshold, or are only effective for specific modulation formats such as BPSK and QPSK but not for other formats which must also be supported by the same product.

While some of the above mentioned techniques can be used, they may not be effective for newer systems capable of increased bandwidth and increased modulation. In other words, application of the currently known techniques for frequency offset estimation could result in a very slow data recovery time at the coherent receiver 34, or worse, the coherent receiver 34 may simply fail.

It is, therefore, desirable to provide a fine LOFO estimator system and method that is simple to implement, accurate in fine frequency offset estimating, and universal such that it is compatible with all systems.

SUMMARY

It is an object of the present disclosure to obviate or mitigate at least one disadvantage of previous fine frequency offset estimation techniques.

In a first aspect, the present disclosure provides a method for estimating a frequency offset of a signal received at a coherent receiver, comprising: receiving a plurality of equalized symbols; processing a probability mass function (PMF) of the plurality of equalized symbols to provide a summation of square of PMF values at each of the a plurality of frequencies; identifying one frequency corresponding to a maximum value of the summation; and setting the frequency offset of the coherent receiver to the identified frequency.

In a second aspect, the present disclosure provides a frequency offset estimator for a coherent receiver, comprising: a probability mass function (PMF) extractor configured to determine phases of a plurality of equalized symbols and to determine individual probability mass function values of the phases at each frequency within a range of frequencies; a PMF processor configured to square and sum the individual probability mass function values to provide a summation of square of PMF values for each frequency; and a PMF identifier configured to identify the maximum of the summation and a corresponding frequency, the corresponding frequency being an estimated frequency offset for the coherent receiver.

In a third aspect, the present disclosure provides a coherent optical transportation link, comprising: a transmitter for generating an optical signal; an optical channel configured to receive and transport the optical signal of the transmitter; and a coherent receiver for receiving the optical signal from the optical channel and configured to provide a plurality of equalized symbols corresponding to the optical signal, the coherent receiver including a frequency offset estimator configured to process a probability mass function (PMF) of the plurality of equalized symbols to provide a summation of square of PMF values at each of a plurality of frequencies, and configured to identify one frequency corresponding to a maximum value of the summation, and a carrier phase recovery circuit configured to correct a phase of the equalized symbols based on the one frequency.

In a fourth aspect, the present disclosure provides a method for estimating a frequency offset of a signal received at a coherent receiver, comprising: receiving a plurality of equalized symbols; processing a probability mass function (PMF) of the plurality of equalized symbols to provide a summation of a function of PMF values at each of the a plurality of frequencies where the function is one of a strictly concave function between 0 and 1, and a strictly convex function between 0 and 1; identifying one frequency from the plurality of frequencies based on the summation of the function of the PMF values; and setting the frequency offset of the coherent receiver to the identified frequency.

In a fifth aspect, the present disclosure provides a frequency offset estimator for a coherent receiver, comprising: a probability mass function (PMF) extractor configured to determine phases of a plurality of equalized symbols and to determine individual probability mass function values of the phases at each frequency within a range of frequencies; a PMF processor configured to determine a function of the individual probability mass function values to provide a summation of the function of PMF values for each frequency where the function is one of: strictly concave between 0 and 1; and strictly convex between 0 and 1 and a PMF identifier configured to identify a frequency corresponding to a value of the summation, the frequency being an estimated frequency offset for the coherent receiver.

In a sixth aspect, the present disclosure provides a coherent optical transportation link, comprising: a transmitter for generating an optical signal; an optical channel configured to receive and transport the optical signal of the transmitter; and a coherent receiver for receiving the optical signal from the optical channel and configured to provide a plurality of equalized symbols corresponding to the optical signal, the coherent receiver including a frequency offset estimator configured to process a probability mass function (PMF) of the plurality of equalized symbols to provide a summation of a function of PMF values at each of a plurality of frequencies where the function is concave or convex, and configured to identify one frequency from the summation between 0 and 1, and a carrier phase recovery circuit configured to correct a phase of the equalized symbols based on the one frequency.

Other aspects and features of the present disclosure will become apparent to those ordinarily skilled in the art upon review of the following description of specific embodiments in conjunction with the accompanying figures.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the present disclosure will now be described, by way of example only, with reference to the attached Figures.

FIG. 1 is a data network diagram of the prior art;

FIG. 2 is a diagram of an optical data transportation link of the prior art;

FIG. 3A is an example phase constellation diagram showing a uniform distribution of phases of output symbols;

FIG. 3B is an example phase constellation diagram showing non-uniform distribution of phases of output symbols;

FIG. 4A is an example plot of PMF versus K sectors at a frequency other than the actual frequency offset;

FIG. 4B is an example plot of PMF versus K sectors at a frequency corresponding to the actual frequency offset;

FIG. 5 is a block diagram of an example coherent optical transportation link according to a present embodiment;

FIG. 6 is a block diagram of example data recovery circuitry used in the system of FIG. 5, according to a present embodiment;

FIG. 7 is a circuit schematic of an example 2^(nd) order PLL used in the carrier recovery circuitry of FIG. 6, according to a present embodiment;

FIG. 8 is a flow chart of a method for estimating actual frequency offset using a convex function p_(i) ^(2.),

FIG. 9 is a flow chart of a method for estimating actual frequency offset using a convex or concave function ƒ(p);

FIG. 10 is a block diagram of the FO estimator of FIG. 6, according to a present embodiment;

FIG. 11 is a block diagram of the PMF extractor of FIG. 9, according to a present embodiment;

FIG. 12 is a flow chart of a first method for estimating actual frequency offset of a signal;

FIG. 13 is a flow chart of a second method for estimating actual frequency offset of a signal, and

FIG. 14 is a plot of experimental data using the previously described frequency offset estimation embodiments.

DETAILED DESCRIPTION

Although the embodiments and its advantages have been described in detail, it should be understood that various changes, substitutions and alterations can be made herein without departing from the invention as defined by the appended claims. Moreover, the scope of the present application is not intended to be limited to the particular embodiments of the process, machine, manufacture, composition of matter, means, methods and steps described in the specification. As one of ordinary skill in the art will readily appreciate from the disclosure of the present invention, processes, machines, manufacture, compositions of matter, means, methods, or steps, presently existing or later to be developed, that perform substantially the same function or achieve substantially the same result as the corresponding embodiments described herein may be utilized according to the present invention. Accordingly, the appended claims are intended to include within their scope such processes, machines, manufacture, compositions of matter, means, methods, or steps.

The present disclosure provides a method and system for fine estimation of a local oscillator frequency offset of a received signal at a coherent receiver, by evaluating the probability mass function (PMF) of the signal phase of equalized symbols at different frequencies. At frequencies other than the actual frequency offset, the signal phase is uniformly distributed in [−π,π] such that the summation of square of PMF (PMF sum-square) values is minimized. However at the actual frequency offset, the signal phase is no longer uniformly distributed over [−π,π]; in other words the signal phase will take some specific values in [−π,π], therefore a peak PMF sum-square value will result. This peak PMF value provides an indication of the actual offset frequency of the received signal.

The presently described embodiments utilize the PMF of the phase of the output symbols to determine the actual frequency offset at the coherent receiver. It is noted that the present embodiments are described within the context of coherent optical receiver systems, but the embodiments are equally applicable to wireless or other electrically wired receiver systems which employ a coherent receiver.

Prior to a detailed discussion of method and apparatus embodiments for determining the actual frequency offset in a coherent receiver, a further explanation of the relationship between PMF and output signal phase follows.

FIG. 3A is an example phase constellation diagram for a set of output symbols at a specific frequency of evaluation. In the example of FIG. 3A, the phase constellation has been divided into K=10 different sectors, or bins, and it is assumed that the signal phases of output symbols at a specific frequency of the coherent receiver has been determined and plotted on this phase constellation diagram. The resulting plot in the example of FIG. 3A is intended to show a uniform distribution of the symbol phases in the range of [−π,π], and thus appears as a solid circle 40 if sufficient symbols are evaluated. This means there is a substantially uniform distribution PMF for the phases of the output symbols to be in each of the K sectors. If the PMF of the phase of the output symbols in the coherent receiver is represented by p_(i)(individual probability mass function values), then the summation of p_(i) (Σp_(i))=1, where p_(i≧)0. To minimize Σp_(i) ², using Lagrange multipliers, one can show that the uniform distribution, i.e. all equal p_(i), minimizes Σp_(i) ². This uniform distribution of the phases of the output symbols corresponds to a situation where frequency offset is not the actual frequency offset of the received signal.

Alternatively, any function ƒ(p) of the PMF values can be utilized, as long as the function is either concave over the entire range of probabilities 0<=(p)=<1, or convex over the entire range of probabilities 0 21=p=<1. If the function is convex (e.g., ƒ(p)=p²), the summation will have a peak at the frequency offset, as shown in FIG. 13. If the function is concave, the summation will have a notch at the frequency offset. The mathematical definition of positive/negative concavity is that the derivative dƒ(p)/dp is a one-to-one function of p. Equivalently, dƒ(p)/dp is either monotonically strictly increasing or monotonically strictly decreasing (or equivalently,

$\left. {{\frac{^{2}{f(p)}}{p^{2}} > 0},{\forall{{p\mspace{14mu} {or}\mspace{14mu} \frac{^{2}{f(p)}}{p^{2}}} < 0}},{\forall p}} \right).$

These conditions have to hold for at least the range 0<=p=<1. In the description below, some examples will be given using f(p)=p². A person of skill in the art will understand how to implement these examples using other strictly concave or strictly convex functions f(p).

In contrast, FIG. 3B is an example phase constellation diagram for a set of output symbols at the actual frequency offset. At the actual frequency offset of the received signal, the phases of the output symbols will appear at M sectors out of K sectors, where M<K. In the present example of FIG. 3B, the phases of the output symbols will appear at K=3, K=5, K=7 and K=10, but will not appear in the remaining sectors. Accordingly, the phases are not uniformly distributed as in the example of FIG. 3A, and the Σp_(i) ² of FIG. 3B results in a peak value that is greater than that of FIG. 3A. Therefore, by defining a local oscillator frequency offset evaluation (LOFOE) criterion as J_(DFS)(f_(DFS))=Σp_(i) ² or in general Σƒ(p), where f_(DFS) is the sweep frequency, a peak in the LOFOE criterion J_(DFS) will be observed at the sweep index representing the actual frequency offset (FO). It is noted that the LOFOE criterion JDFS is a PMF based value. A sweep frequency can be one of a range of different frequencies separated by a predetermined step size, used to evaluate a particular J_(DFS.) A sweep index designates each of these distinct frequencies with an arbitrary integer number. From this point forward, JDFS is referred to as a PMF sum-square value.

FIG. 4A is an experimental plot of PMF for the different K sectors for a frequency that is not the actual frequency offset, using a limited set of output symbols. The PMF here correlates to a more uniform distribution of the phases. FIG. 4B is an experimental plot of PMF for the different K sectors for a frequency corresponding to the actual frequency offset of the received signal at the coherent receiver. It is clearly shown that the PMF correlates to a non-uniform distribution indicative of a frequency at or close to the actual frequency offset. It should be noted that the plots of FIGS. 4A and 4B do not represent the example phase plots of FIGS. 3A and 3B.

The value of K is set based on the desired level of phase detection resolution. A higher K results in a larger number of smaller sectors, which will increase accuracy of the actual frequency offset estimation. Generally, as higher K is used, more memory is required as will be discussed later. A low K value may not be useful as the resolution could be insufficient to distinguish between one frequency where the phase distribution of the output symbols is distributed uniformly and another frequency corresponding to the actual frequency offset where the phase distribution of the output symbols is distributed non-uniformly. Therefore the lower limit of K for a specific coherent receiver system can be set as the lowest integer value before a non-uniform phase distribution can no longer be distinguished from a uniform phase distribution.

With the principles above in mind, embodiments for a method and apparatus for determining the actual frequency offset of a signal received by a coherent receiver can be developed. FIG. 5 is a block diagram of a coherent optical transportation link which uses the method and apparatus according to the present embodiments. The coherent optical transportation link 100 includes a transmitter 102 and a coherent receiver 104 communicatively coupled through an optical channel 106. The optical channel 106 includes planted fiber 108, optical filters 110 and optical amplifiers 112. The coherent receiver 104 includes an integrated coherent receiver 114, an analog to digital converter (ADC) 116, and a digital signal processor (DSP) unit 118. In fiber optics digital coherent receivers, such as coherent receiver 104, quasi-static channel impairments and also component impairments such as chromatic dispersion (CD), state-of-polarization (SOP) rotations, polarization mode dispersion (PMD), polarization-dependent loss (PDL), laser phase noise, PPM, frequency offset, I-Q and X-Y delay, I-Q imbalance, etc. are compensated digitally in DSP unit 118. According to the present embodiments, a frequency offset (FO) determinator that is configured to evaluate the previously mentioned PMF sum-square value J_(DFS)(f_(DFS))=Σp_(i) ² or in general Σƒ(p). For determining the actual frequency offset of a received signal, is implemented in the DSP unit 118 with transistor circuitry and/or predetermined circuit blocks having specific functions.

FIG. 6 is an embodiment of a block diagram of data recovery circuitry in the DSP unit 118 of FIG. 5. In the presently shown data recovery circuit embodiment of FIG. 6, different circuit blocks compensate individual impairments in an efficient way to minimize the complexity of the overall circuit. Alternately, it is possible to compensate for all impairments in one equalizer circuit block which would require a complicated MIMO-IIR adaptive equalizer with a large number of taps. The data recovery circuit 200 of FIG. 6 includes frequency domain equalizers (FDEQ) 202 and 204, a time domain equalizer such as MIMO-FIR 206, a carrier phase recovery circuit 208, a forward error correction (FEC) circuit 210, an FO estimator 212 and switches 214.

Since CD is a quasi-deterministic impairment with very long echo, CD compensation (CDC) is done in a static frequency domain equalizer, namely by FDEQ 202 and 204. FDEQ 202 compensates for CD and match filtering of the horizontal polarization of the received signal, while FDEQ 204 compensates for CD and match filtering of the vertical polarization of the received signal. Afterwards, polarization dependent impairments are compensated through an adaptive time-domain butterfly structure of MIMO-FIR 206. More specifically, MIMO-FIR 206 executes SOP, PDL and PMD equalization, by example. Then carrier phase recovery circuit 208 corrects for laser line-width and phase noise of the equalized signals from MIMO-FIR 206 in each polarization. The FEC circuit 210 then executes error correction upon actual data.

The carrier phase recovery circuit 208 includes a 2^(nd) order PLL (phase locked loop) which is used for correcting the phase of the received signal relative to a reference frequency estimation provided by the FO estimator 212. For reference, FIG. 7 shows a 2^(nd) order PLL of a particular configuration which could be used in carrier phase recovery circuit 208. In FIG. 7, φ₁ represents phase correction error, φ₂ represents frequency offset correction. The PLL circuit of FIG. 7 adjusts φ₂=2πf_(DFS)/f_(Baud,) where f_(DFS) is provided by FO estimator 212 of FIG. 6, and f_(Baud) is the baud rate of the system. In FIGS. 7, μ_(φ)and μ_(φ2) are small step size values in LMS adaptation for the phase and frequency track, respectively. Δφ is the error signal of PLL that is the difference between the received signal phase and estimated phase. φ₁+φ₂ is the estimated phase from PLL.

In the present embodiment, the FO estimator 212 includes PMF evaluation circuitry for executing estimation of the actual frequency offset based on the earlier discussed J_(DFS)(f_(DFS))=Σp_(i) ² or in general Σƒ(p) criteria for estimating the actual frequency offset of the received signal. The switches 214 represent the functional turning on and off of the FO estimator 212. More specifically, the FO estimator 212 is used during initial signal acquisition of the coherent receiver, such as after a reset event of the coherent receiver where receiving operations are ceased. Accordingly in the example of FIG. 6, switches 214 are closed to couple the signal output from carrier phase recovery circuit 208 to FO estimator 212 after a reset event, and opened after the FO estimator 212 has provided the actual frequency offset to carrier phase recovery circuit 208. While the FO estimator 212 is enabled, it evaluates the output of the carrier phase recovery circuit 208 at different frequencies to eventually determine the actual frequency offset. Once determined, this actual frequency offset is stored and used by carrier phase recovery circuit 208 to extract data. It is noted that the FO estimator 212 can be used with any carrier phase recovery circuit similar to the one shown and described in the embodiment of FIG. 6.

FIG. 8 is a flow chart which outlines the method embodiment of estimating the actual frequency offset using the summation of the squares of PMF values, as executed by FO estimator 212 of FIG. 6. More specifically, the circuits and logic of FO estimator 212 are configured for executing the method embodiment of FIG. 8. The method starts with a reset event at 300, which can include powering up the coherent receiver. Most coherent receiver specifications provided by the manufacturer indicate a coarse frequency offset error range f_(coarse), such as 700 MHz for example. Alternately, a supplemental circuit can be used to provide a coarse estimate of the frequency offset with a similar error range. With this coarse frequency offset error range, a frequency sweep range of f_(min) to f_(max) is set, where f_(min) is set as −f_(coarse) and f_(max) is set as +f_(coarse). Also, a frequency step size is set based on the best resolution of the system. Then the method proceeds to 302 where the output data of carrier phase recovery circuit 208 is iteratively sampled at all the different frequencies f, where f is stepped, or sweeped, from f_(min) to f_(max) by the step size. More specifically, the 2^(nd) order PLL is provided with each different frequency for operating on the received signal.

Following at 304, J_(DFS)(f_(DFS))= is calculated for each frequency iteration of f_(DFS). Recall that JDFS is a PMF sum-square value. This PMF value and its corresponding frequency is stored in memory. Then proceeding to 306, the frequency having the largest J_(DFS) value is identified. At 308, the actual frequency offset is set and provided to carrier phase recovery circuit 208 for normal receiving operation. Then the FO estimator 212 can be disabled or turned off as it is no longer required during normal operation of the coherent receiver. Therefore, the FO estimator 212 can be seen as operating during a signal acquisition phase of operation of the coherent receiver.

FIG. 9 is a flow chart which outlines a method embodiment of estimating the actual frequency offset using a concave or convex function Σƒ(p), as executed by FO estimator 212 of FIG. 6. The method shown in FIG. 9 is similar to FIG. 8, except that the function ƒ(p) is either concave over the entire range of probabilities 0<=p=<1, or convex over the entire range of probabilities 0 <=p=<1. Following 302, J_(DFS) is calculated at 305 where J_(DFS)(f_(DFS))=Σƒ(p) for each frequency iteration of f_(DFS). This PMF value and its corresponding frequency is stored in memory. Then proceeding to 307, a frequency associated with a J_(DFS) value is identified. The identified frequency is associated with the maximum of the summation in the case where f(p) is a convex function; and is associated with the minimum of the summation in the case where f(p) is a concave function. At 308, the actual frequency offset is set and provided to carrier phase recovery circuit 208 for normal receiving operation.

FIG. 10 is a block diagram showing an embodiment of the FO estimator 212 of FIG. 6, according to a present embodiment. In order to simplify the schematic, block 400 is a combination of both MIMO-FIR 206 and carrier phase recovery circuit 208 of FIG. 6, and is simply referred to as the MIMO-FIR and phase recovery block 400.

The present FO estimator embodiment includes PMF extractors 402, 404, PMF processors 406, 408, a local summer 410, a global summer 412, a PMF identifier 414, a frequency sweeper 416 and frequency offset setting circuits 418 and 419. PMF extractor 402 and PMF processor 406 operate on one polarization of the received signal while PMF extractor 404 and PMF processor 408 operate on another polarization of the received signal. The group of circuit blocks 400, 402, 404, 406 and 408 can be referred to as a single PMF processing branch. Some coherent receivers may have multiple PMF processing branches having circuit blocks identical to circuit blocks 400, 402, 404, 406 and 408, but operating concurrently on different sets of data. Such a level of parallelism can be used when a single processor branch is not fast enough to process the stream of input data. Following is a discussion of PMF extractors 402, 404, PMF processors 406, 408, PMF identifier 414, frequency sweeper 416 and frequency offset setting circuits 418 and 419.

During the signal acquisition phase of operation, the frequency sweeper 416 is responsible for setting different f_(DFS) frequencies at predetermined step sizes, and executes the frequency sweeping function discussed at step 302 of the method embodiments of FIGS. 8 and 9. Once f_(DFS) is set, frequency offset setting circuit 419 will set φ₂ using the f_(DFS) set by frequency sweeper 416. The MIMO-FIR and phase recovery block 400 then operates using the set φ₂, and provides a polarized signal (Xe) to PMF extractor 402, where the PMF of the equalized signal phase is extracted for each frame of a data burst, at the specific f_(DFS) frequency. This can be done for each symbol, by having circuits detect the phase and identifying which sectors of the phase constellation the phases are distributed (ie. as shown in FIG. 3A and FIG. 3B). PMF extractor 402 tracks the number of times a phase is identified in each sector out of K sectors. Table 1 below shows an example extracted PMF of phases of symbols with K=10, where the left-most column identifies a K identifier, the middle column lists the constellation range for the corresponding sector, and the right-most column lists the count for identified phases of symbols in each of the phase constellation sectors.

TABLE 1 Phase Constellation Count K Sectors (p_(i)) 1 0 to π/5 5 2 π/5 to 2π/5 3 3 2π/5 to 3π/5 8 4 3π/5 to 4π/5 6 5 4π/5 to π 6 6 π to 6π/5 4 7 6π/5 to 7π/5 3 8 7π/5 to 8π/5 5 9 8π/5 to 9π/5 4 10 9π/5 to 2π 9

As more symbols are evaluated by PMF extractor 402, the counts will increase. Using the previous example of FIG. 3A where a uniform phase distribution is observed, the counts in Table 1 for all the sectors will be substantially close to each other. On the other hand, using the previous example of FIG. 3B where a non-uniform phase distribution is observed, the counts across all K sectors are not close. Once a specific amount of symbols have been evaluated, such as one frame of symbols, the collected counts are then provided to PMF processor 406. PMF processor 406 then executes the mathematical function of J_(DFS) _(_) _(x)(f_(DFS))=Σp_(i) ² or in general Σƒ(p) at the present offset frequency of f_(DFS), which corresponds to step 304 of FIG. 8 or step 305 of FIG. 9 respectively. Using the example of Table 1, where J_(DFS) _(_) _(x)(f_(DFS))=Σp_(i) ²=5²+3²+8²+6² . . . +4²+9². PMF extractor 404 and PMF processor 408 operate concurrently on the other polarization with PMF extractor 402 and PMF processor 406 in exactly the same way, except that PMF processor 408 provides J_(DFS) _(_) _(y)(f_(DFS)). Both J_(DFS) _(_) _(x)(f_(DFS)) and J_(DFS) _(_) _(y)(f_(DFS)) are simply added together at local summer 410 to yield J_(DFS) _(_) _(xy)(f_(DFS)) as both polarizations are facing the same frequency offset. It is noted that PMF extractor 404 and PMF processor 408 are not required, but are included in the present embodiment to improve accuracy of FO estimation.

Assuming that the other PMF process branches 420 and 422 are not present, or not being used, the PMF processor output J_(DFS) _(_) _(xy)(f_(DFS)) is provided to PMF identifier 414. The PMF identifier 414 keeps track of J_(DFS) _(_) _(xy)(f_(DFS)) value that is maximum (if a convex function f(p) was used) or a minimum (if a concave function f(p) was used) and the corresponding f_(DFS) that resulted in it. This generally corresponds to step 306 of FIG. 8 and FIG. 9. This iteration for one f_(DFS) is now complete, and frequency sweeper 416 changes f_(DFS) to the next frequency. This next frequency can be the previous frequency plus a predetermined step size, and is referred to as the next frequency index. The previously described operations of PMF extractors 402, 404 and PMF processors 406, 408 then repeats again such that a new J_(DFS) _(_) _(xy)(f_(DFS)) is provided to PMF identifier 414. Eventually J_(DFS) _(_) _(xy)(f_(DFS)) at all frequency indices within the range of f_(min) to f_(max) are provided, and PMF identifier 414 then sets the actual frequency offset to be the frequency where the largest (or smallest) J_(DFS) _(_) _(xy)(f_(DFS)) value occurred. This corresponds to step 308 of FIG. 8 and FIG. 9. Now the frequency offset setting circuit 418 is set using this actual frequency offset and the signal acquisition phase ends so that normal receiving operations can proceed. In summary, the FO estimator of the embodiment of FIG. 10 processes PMF of the equalized symbols to provide a summation of a concave or convex function of PMF values at different frequencies, and identifies one frequency corresponding to a maximized summation of a concave or convex function of PMF values.

In alternate embodiments, any one or more of parallel PMF processing branches 420 and 422 can be used to improve accuracy of the final J_(DFS) _(_) _(xy)(f_(DFS)) values. Since each PMF processing branch is operating at the same f_(DFS) and φ₂ but on different sets of data, the global summer 412 is used to add the J_(DFS) _(_) _(xy)(f_(DFS)) values from the output of each PMF processing branch together. This global J_(DFS) _(—xy) (f_(DFS)) value is provided to PMF identifier 414, and the process is repeated again for a different f_(DFS). More data allows for a larger difference between a J_(DFS) _(—xy) (f_(DFS)) value from a uniform phase distribution and a J_(DFS) _(_) _(xy)(f_(DFS)) value from a non-uniform phase distribution corresponding to the actual frequency offset. It should be appreciated that such a larger difference is easier to detect. In fact, a single pairing of one PMF extractor 402 and one PMF processor 406 is sufficient for estimating the FO, and different pairings from any combination of PMF processing branches 420 and 422 can be concurrently active in the FO estimation embodiments.

Accordingly, further robustness can be gained by having the FO estimator 212 process multiple bursts of blocks, instead of just a single burst of blocks. In summary, the final J_(DFS) _(_) _(xy)(f_(DFS)) for all parallel PMF processing branches can be expressed with equation 1 below:

$\begin{matrix} {{{J_{DFSTOTAL}\left( f_{DFS} \right)} = {\sum\limits_{{burst} = 1}^{nBursts}\; {\sum\limits_{{processor} = 1}^{nProc}\; {\sum\limits_{j = 1}^{nPol}\; {\sum\limits_{i = 1}^{K}\; {p_{i}^{2}\left( f_{DFS} \right)}}}}}}{{J_{DFSTOTAL}\left( f_{DFS} \right)} = {\sum\limits_{{burst} = 1}^{nBursts}\; {\sum\limits_{{processor} = 1}^{nProc}\; {\sum\limits_{j = 1}^{nPol}\; {\sum\limits_{i = 1}^{K}\; {{f(p)}\left( f_{DFS} \right)}}}}}}} & {{Equation}\mspace{14mu} 1} \end{matrix}$

where K is the resolution of PMF of signal phase; nPol is the number of polarizations that is 2 for polarization multiplexed systems and 1 for single polarization transmission; nProc is the number of parallel TDEQ and CR processors or branches in the DSP; nBursts is number of bursts of blocks involved in each calculation, where nBursts should be set based on the system specifications.

FIG. 11 is a block diagram showing further details of PMF extractors 402 or 404, according to a present embodiment. In this embodiment, PMF extractor 402 includes a K bin quantizer 450 and a counters block 452. The K bin quantizer 450 is responsible for detecting a phase of the input signal and then determining which of the K sectors, or phase bins, the phase belongs in. The p(L)++ circuit 452 is a counters block, which can include memory or registers for keeping count of the number of instances a phase is detected as belonging in a particular phase bin (or K sector). Alternately, K bin quantizer 450 can be implemented as a look up table (LUT). For example, by multiplying the detected phase φ with K/(2π(φ×K/(2π)), the resulting value can be rounded to correspond with a table having K entries. For example, if round(φ×K/(2π) )=3, then the K=3 entry in the table is incremented by 1. In both embodiments, memory is required to store the counts.

The previously discussed embodiments of the FO estimator, such as the one shown in FIG. 10 by example, can be used in a coherent optical transportation link. Such a coherent optical transportation link was previously shown in the embodiment of FIG. 5. The presently described coherent optical transportation link embodiment would include the transmitter 102, the optical channel 106 and the coherent receiver 104. The transmitter 102 generates an optical signal, which is received and transported by the optical channel 106. The transmitter 102 can be located at a source location such as a service provider 10, a regional node 14 or a base station 16 as shown in FIG. 1, and the optical channel 106 can be represented by the data cables 18, 20 and 22.

The coherent receiver 104 receives the optical signal from the optical channel 106, and is configured to provide equalized symbols corresponding to the optical signal using circuits such as frequency domain equalizers (FDEQ) 202 and 204 and MIMO-FIR 206, previously shown in the embodiment of FIG. 6. The coherent receiver 104 would include a frequency offset estimator such as the frequency offset estimator 212 embodiment of FIG. 6 and the embodiment of FIG. 10, and a carrier phase recovery circuit such as the one shown by the carrier phase recovery circuit 208 embodiment of FIG. 6. The FO estimator in the presently described coherent optical transportation link embodiment processes probability mass function (PMF) of the equalized symbols for the purposes of providing a summation a convex or concave function of PMF values at different frequencies, and identifies one frequency corresponding to a maximized summation of square of PMF values. The carrier phase recovery circuit in the presently described coherent optical transportation link embodiment corrects a phase of the equalized symbols based on the identified one frequency.

With reference to FIG. 12 and FIG. 13, detailed flow charts of the methods for estimating actual frequency offset of a signal in a coherent receiver using PMF of signal phase are described. For example, the following method embodiment can be executed in the circuits shown in FIGS. 5, 6 and 10. More specifically, the method embodiments of FIG. 12 and FIG. 13 can be executed in the DSP 118 of the embodiment of FIG. 5, in the FO estimator 212 of the embodiment of embodiment of FIG. 6, and in the PMF extractor embodiment of FIG. 10.

The method of FIG. 12 begins at 500 after a reset event, where foFs is set to f_(min), J_(max) and J_(DFS) are set to 0, f_(est) is set to f_(min), and iBurst is set to 0. The variable f_(est) will eventually be the actual frequency offset, f_(min) is the minimum frequency to use, J_(max) stores the greatest PMF value, and the PMF sum-square value J_(DFS) is a currently evaluated PMF processor output. Following at 502, φ₂ is set to 2π×f_(DFS)/f_(Baud) for the 2^(nd) order PLL of the carrier phase recovery circuit 208, and the iBurst value is incremented. For example, the MIMO-FIR and phase recovery block 400 is now set to operate with the f_(DFS) and φ₂ values. As output symbols are provided from MIMO-FIR and phase recovery block 400, the PMF of the output phase for each symbol is determined at 504, and represented as p_(i). This is where counts of the phase in each of the K sectors of the phase constellation sectors are accumulated. Following at 506 in FIG. 12, a PMF processor calculation using a convex function such as J_(DFS)=J_(DFS)+ΣP_(i) ² is executed for the current burst of blocks. If at 508 the current burst number iBurst is not greater than a maximum burst number nBurst, then the method returns to 502 to receive a subsequent burst of blocks to evaluate. As the method loops through 502, 504 and 506 under the same f_(DFS) and φ₂ settings for each successive burst of blocks, J_(DFS) continues increasing in value.

Once current burst number iBurst is greater than a maximum burst number nBurst, then the method proceeds to 510. A comparison between the current J_(DFS) and J_(max) is made at 510. Because this first iteration has J_(max)=0 and J_(DFS) is surely >0, J_(max) is set as J_(DFS), and f_(est) is set as f_(DFS) at 516. In other words, the maximum J_(DFS) is recorded with its corresponding frequency, and any previous lower J_(DFS) and corresponding frequency value is discarded or ignored. If at 510 J_(DFS) is less than J_(max), then the current f_(DFS) frequency is of no interest, and the method proceeds to 512 where parameters J_(DFS) and iBurst are reset to 0, and f_(DFS) is incremented by the predetermined frequency step size. A comparison of the newly incremented f_(DFS) is compared to f_(max) at 514. If f_(DFS) has not exceeded f_(max), then there are still more frequencies to determine PMF of the output phase at, so the method returns to 502 with a new f_(DFS) value. Otherwise, the method proceeds to 518 as all the frequency indices have been swept. By 518, the largest JDFS value has been stored as J_(max), and its corresponding frequency has been stored as f_(est),which is reported and set as the actual frequency offset for the coherent receiver. Normal receiving operation of the coherent receiver can now proceed.

With reference to FIG. 13, the method begins at 520 after a reset event, where f_(DFS) is set to f_(min), and J_(DFS) are set to 0, f_(est) is set to f_(min), and iBurst is set to 0. The variable f_(est) will eventually be the actual frequency offset, f_(min) is the minimum frequency to use, J_(min) stores the smallest PMF value, and the PMF function value J_(DFS) is a currently evaluated PMF processor output. Following at 522, φ₂ is set to 2π×f_(DFS)/f_(Baud) for the 2^(nd) order PLL of the carrier phase recovery circuit 208, and the iBurst value is incremented. For example, the MIMO-FIR and phase recovery block 400 is now set to operate with the f_(DFS) and φ₂ values. As output symbols are provided from MIMO-FIR and phase recovery block 400, the PMF of the output phase for each symbol is determined at 524, and represented as p_(i). This is where counts of the phase in each of the K sectors of the phase constellation sectors are accumulated. Following at 526, a PMF processor calculation of J_(DFS)=J_(DFS)+Σƒ(p) is executed for the current burst block, using a concave function f(p). If at 528 the current burst number iBurst is not greater than a maximum burst number nBurst, then the method returns to 522 to receive a subsequent burst of blocks to evaluate. As the method loops through 522, 524 and 526 under the same f_(DFS) and φ₂ settings for each successive burst of blocks, J_(DFS) continues increasing in value.

A comparison between the current J_(DFS) and J_(min) is made at 530. Because this first iteration has J_(min)=0 and J_(DFS) is surely>0, J_(min) is set as JDFS, and f_(est) is set as f_(DFS) at 536. In other words, the minimum J_(DFS) is recorded with its corresponding frequency, and any previous higher J_(DFS) and corresponding frequency value is discarded or ignored. If at 530 J_(DFS) is greater than J_(min), then the current f_(DFS) frequency is of no interest, and the method proceeds to 532 where parameters J_(DFS) and iBurst are reset to 0, and f_(DFS) is incremented by the predetermined frequency step size. A comparison of the newly incremented f_(DFS) is compared to f_(min) at 534. If f_(DFS) has not exceeded f_(max), then there are still more frequencies to determine PMF of the output phase at, so the method returns to 522 with a new f_(DFS) value. Otherwise, the method proceeds to 538 as all the frequency indices have been swept. By 538, the largest J_(DFS) value has been stored as Jmin , and its corresponding frequency has been stored as f_(est), which is reported and set as the actual frequency offset for the coherent receiver. Normal receiving operation of the coherent receiver can now proceed.

The previously described FO estimator embodiments have been implemented and tested to demonstrate the effectiveness of using PMF of signal output phase for estimating the actual frequency offset of a signal received by a coherent receiver. FIG. 14 is a plot of the PMF processor output (J_(DFS)) at different f_(DFS) frequencies where J_(DFS)(f_(DFS))=ΣP_(i) ². The single peak value is clearly evident in FIG. 14, and the frequency offset error is about 1 MHz, well below the tolerated maximum of 10 MHz. In similar test using prior art frequency offset estimation methods, the estimation error is much larger than the tolerable limits, and system fails to recover the data.

In summary, the previously described frequency offset estimation method embodiment and system embodiment for coherent digital receivers estimates the offset frequency with higher speed, more robustness and accuracy over currently known methods. The present embodiments using PMF of signal phase can be used with any type of signaling, such as for example RRC, RC, NRZ and RZ67. The present embodiments using PMF of signal phase are compatible with all modulation schemes, including for example BPSK, QPSK, 8QAM,16QAM and 64QAM, and with all pre-codings, pre-compensations, quantizations, and different sources of noises which can include amplified spontaneous emission (ASE) and phase noise by example. The present embodiments are compatible with any DSP algorithm, insensitive to narrow electrical bandwidth, large number of Wavelength Selective Switches (WSS), larger LOFO, large ASE and large channel impairments. The present embodiments are not complex, are hardware friendly, and features fast convergence as less bursts are required to determine the offset frequency.

The previously described embodiments have been illustrated in the context of polarization-multiplexed coherent optical transmission, however, they can be used in single-polarization coherent optical transmission as well. Furthermore, the previously described embodiments can be used in traditional wired and wireless communications systems that use a coherent receiver. More specifically, any coherent system can include the FO estimator circuits taught in the previous embodiments, and with an existing frequency corrector, can sweep the range of all possible operating frequencies. Based on the PMF sum-square output, referred to as the PMF processor output, FO can be estimated.

In the preceding description, for purposes of explanation, numerous details are set forth in order to provide a thorough understanding of the embodiments. However, it will be apparent to one skilled in the art that these specific details are not required. In other instances, well-known electrical structures and circuits are shown in block diagram form in order not to obscure the understanding. For example, specific details are not provided as to whether the embodiments described herein are implemented as a software routine, hardware circuit, firmware, or a combination thereof.

Embodiments of the disclosure can be represented as a computer program product stored in a machine-readable medium (also referred to as a computer-readable medium, a processor-readable medium, or a computer usable medium having a computer-readable program code embodied therein). The machine-readable medium can be any suitable tangible, non-transitory medium, including magnetic, optical, or electrical storage medium including a diskette, compact disk read only memory (CD-ROM), memory device (volatile or non-volatile), or similar storage mechanism. The machine-readable medium can contain various sets of instructions, code sequences, configuration information, or other data, which, when executed, cause a processor to perform steps in a method according to an embodiment of the disclosure. Those of ordinary skill in the art will appreciate that other instructions and operations necessary to implement the described implementations can also be stored on the machine-readable medium. The instructions stored on the machine-readable medium can be executed by a processor or other suitable processing device, and can interface with circuitry to perform the described tasks.

The above-described embodiments are intended to be examples only. Alterations, modifications and variations can be effected to the particular embodiments by those of skill in the art. The scope of the claims should not be limited by the particular embodiments set forth herein, but should be construed in a manner consistent with the specification as a whole. 

1-20. (canceled)
 21. A method for estimating a frequency offset of a signal received at a coherent receiver, comprising: receiving a plurality of equalized symbols; processing a probability mass function (PMF) of the plurality of equalized symbols to provide a summation of a function of PMF values at each of the a plurality of frequencies where the function is one of a strictly concave function between 0 and 1, and a strictly convex function between 0 and 1; identifying one frequency from the plurality of frequencies based on the summation of the function of the PMF values; and setting the frequency offset of the coherent receiver to the identified frequency.
 22. The method of claim 21, wherein the function is a convex function, and the one frequency is identified by the maximum of the summation.
 23. The method of claim 21 wherein the function is a concave function, and the one frequency is identified by the minimum of the summation.
 24. The method of claim 21, further comprising: resetting the coherent receiver before iteratively receiving equalized symbols in a signal acquisition phase of operation; and operating the coherent receiver with the frequency offset in a normal phase of operation.
 25. The method of claim 21, wherein processing includes detecting phases of a frame of a data burst; and identifying in which K sectors of a phase constellation the detected phases are distributed, wherein K is a finite integer greater than
 1. 26. The method of claim 25, wherein processing further includes counting the distribution of the detected phases.
 27. The method of claim 26, wherein processing further includes calculating a summation of the function of the distribution of the detected phases, the summation of the function of the distribution of the detected phases corresponding to the summation of the function of PMF values.
 28. The method of claim 27, wherein said identifying one frequency further includes comparing the summation of the function of PMF values to each other to identify the maximized summation of the function of the PMF values and the corresponding one frequency.
 29. The method of claim 21, wherein the equalized symbols include symbols from first and second polarization components of the signal.
 30. The method of claim 26, wherein processing further includes concurrently calculating a second summation of the function of the PMF values corresponding to another set of data of the signal at the same frequency, and adding the summation of the function of the PMF values and the second summation of the function of the PMF values together.
 31. A frequency offset estimator for a coherent receiver, comprising: a probability mass function (PMF) extractor configured to determine phases of a plurality of equalized symbols and to determine individual probability mass function values of the phases at each frequency within a range of frequencies; a PMF processor configured to determine a function of the individual probability mass function values to provide a summation of the function of PMF values for each frequency where the function is one of: strictly concave between 0 and 1; and strictly convex between 0 and 1; and a PMF identifier configured to identify a frequency corresponding to a value of the summation, the frequency being an estimated frequency offset for the coherent receiver.
 32. The frequency offset estimator of claim 31, wherein the function is a convex function, and the frequency is identified by a maximum of the summation.
 33. The frequency offset estimator of claim 31, wherein the function is a concave function, and the frequency is identified by a minimum of the summation.
 34. The frequency offset estimator of claim 31, wherein the PMF extractor includes a quantizer for detecting the phases and identifying in which K sectors of a phase constellation the detected phases are distributed, wherein K is a finite integer greater than
 1. 35. The frequency offset estimator of claim 31, wherein the PMF extractor includes counters for counting the distribution of the detected phases; and a memory for storing counts of the distribution of the detected phases.
 36. The frequency offset estimator of claim 35, wherein the PMF extractor and the PMF processor are a first PMF extractor and a first PMF processor, wherein the first PMF extractor receives equalized symbols corresponding to one polarization of a received optical signal and the first PMF processor provides a first summation of the function of PMF values.
 37. The frequency offset estimator of claim 36, further comprising a second PMF extractor and a second PMF processor, wherein the second PMF extractor receives equalized symbols corresponding to another polarization of the received optical signal and the second PMF processor provides a second summation of the function of PMF values.
 38. The frequency offset estimator of claim 37, further comprising a local summer for adding the first summation of the function of PMF values to the second summation of the function of PMF values to provide the summation of the function of PMF values.
 39. The frequency offset estimator of claim 37, wherein the first PMF extractor, the first PMF processor, the second PMF extractor and the second PMF processor are included in a first PMF processing branch for operating on a first set of data, and the frequency offset estimator further includes a second PMF processing branch operating on a second set of the data concurrently as the first PMF processing branch, to provide a third summation of the function of PMF values and a fourth summation of the function of PMF values.
 40. The frequency offset estimator of claim 39, further comprising a summer for adding the first summation of the function of PMF values, the second summation of the function of PMF values, the third summation of the function of PMF values and the fourth summation of the function of PMF values to each other to provide the summation of the function of PMF values.
 41. A coherent optical transportation link, comprising: a transmitter for generating an optical signal; an optical channel configured to receive and transport the optical signal of the transmitter; and a coherent receiver for receiving the optical signal from the optical channel and configured to provide a plurality of equalized symbols corresponding to the optical signal, the coherent receiver including a frequency offset estimator configured to process a probability mass function (PMF) of the plurality of equalized symbols to provide a summation of a function of PMF values at each of a plurality of frequencies where the function is concave or convex, and configured to identify one frequency from the summation between 0 and 1; and a carrier phase recovery circuit configured to correct a phase of the equalized symbols based on the one frequency.
 42. The coherent optical transportation link of claim 41, wherein the one frequency is identified by a maximum of the summation for the convex function.
 43. The coherent optical transportation link of claim 41, wherein the one frequency is identified by a minimum of the summation for the concave function. 